options?
What we don't know is the conversation this crew had with the NY TRACON. I'd lay money that they communicated their need for 31R and the controller responded by telling them they'd have to get at the end of the (very long) line for 22L, including arrivals that weren't even in NY's airspace. In other words, they'd hold until they'd have to divert. And then when they divert and refuel and go back to JFK, instead of getting priority as a diversion, they'd be holding again for 31R. So why would the crew want to talk to the TRACON again? They know they'll be treated as a "paper" emergency and won't get the priority an emergency should receive.
While this seems pretty high-handed, it's pretty sad that the options available to this pilot, if he wished to land his flight at his intended destination, were to accept a direct crosswind of 35 gusting or declare an emergency to get the appropriate runway and fly his own traffic pattern.